✅ Pehle Yeh Aata Hai?
Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:
- 250 ka 20% kitna hai?
- 15, 60 ka kitna percent hai?
- Riya ko 20 mein se 16 aur Tina ko 25 mein se 21 marks mile. Kisne behtar kiya?
Answers dekho
- 20% = 1/5, to 250 ÷ 5 = 50
- 15/60 = 1/4 = 25%
- Riya: 16/20 = 80/100 = 80%. Tina: 21/25 = 84/100 = 84%. Tina ne behtar kiya.
Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 3 — Kisi Cheez Ka Percentage aur Post 7 — Percentage Se Tulna ek baar dekh lijiye, phir yahan wapas aaiye.
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🎬 Kahani: Canteen Mein Daam Badh Gaye!
Monday ko school canteen pe naya rate board laga. Samosa pehle ₹10 ka tha, ab ₹12 ka. Chips ka packet pehle ₹20 ka tha, ab ₹23 ka.
Kabir bola, “Chips sabse zyada mehnga hua, ₹3 badh gaye! Samosa sirf ₹2.”
Zoya ne sir hilaaya, “Ruko! ₹2 ek ₹10 wali cheez pe badhe hain, aur ₹3 ek ₹20 wali cheez pe. Dono ki shuruaati keemat hi alag thi!” 🤔
Yeh to wahi Post 7 wali baat lag rahi hai na, alag-alag totals! To asli mein kiska daam zyada tezi se badha? Aaj seekhenge percentage increase aur decrease, aur aakhir mein Kabir-Zoya ka jhagda bhi suljhayenge. 😉
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📖 Concept: Badlaav Ko “Shuruaati Keemat” Se Naapo
Step 1: Pehle pehchano, badha ya ghata?
Har sawaal mein do value hoti hain: Original (pehle wali / shuruaati) aur New (baad wali).
- New > Original → Increase (badhotri). Samosa ₹10 → ₹12.
- New < Original → Decrease (kami). Jaise pen ₹50 → ₹40.
WHY yeh zaroori hai? Jawab mein humein batana hai ki cheez badhi ya ghati. “20%” akela adhoora hai, “20% badha” ya “20% ghata” poora jawab hai.
Step 2: Badlaav (change) nikaalo
Badi value mein se chhoti value ghatao:
- Increase = New − Original → Samosa: 12 − 10 = ₹2
- Decrease = Original − New → Pen: 50 − 40 = ₹10
WHY? Change hamesha ek positive number ki tarah likhte hain, aur “badha/ghata” shabd se direction batate hain. Isliye badi mein se chhoti ghatate hain.
Step 3: Change ko ORIGINAL se divide karo
Ab poochho: yeh change, shuruaati keemat ka kitna hissa hai?
- Samosa: 2/10
- Chips: 3/20
WHY original se, new se kyun nahi? Kyunki badlaav original se shuru hua. “₹10 wala samosa ₹2 mehnga hua” mein base ₹10 hai. Jaise Post 3 mein “kis cheez ka percent” poocha jaata tha, waise hi yahan “kis keemat pe badha” ka jawab hai: original pe.
Step 4: × 100 karke percentage banao
% Increase = (Increase ÷ Original) × 100
% Decrease = (Decrease ÷ Original) × 100
- Samosa: 2/10 × 100 = 20% increase
- Chips: 3/20 × 100 = 300/20 = 15% increase
WHY × 100? Fraction ko percentage mein badalne ka yahi tareeka hai (Post 3 aur Post 5). Ab dono ka “total” 100 ho gaya, isliye tulna fair hai.
Kabir-Zoya ka faisla: 20% > 15%, isliye samosa zyada tezi se mehnga hua, bhale hi rupayon mein chips ke ₹3 badhe. Zoya sahi thi! ✅
Step 5: Ulta sawaal: % pata hai, nayi value nikaalo
Kabhi sawaal kehta hai: “₹400 ka bag 15% mehnga hua. Nayi keemat?”
- Original ka 15% nikaalo: 400 × 15/100 = ₹60 (yeh increase hai)
- Increase ho to jodo: 400 + 60 = ₹460
Agar 15% sasta hota, to ghatate: 400 − 60 = ₹340.
WHY? “15% badha” ka matlab hai original ke 15% jitna badha. Isliye pehle original ka 15% nikaala, phir use joda ya ghataya.
Step 6: Ek kadam wala shortcut: guna karne wala number (multiplier)
Original ko 100% maano. 15% badha to nayi value = 100% + 15% = 115% of original.
- 15% increase → × 115/100 = × 1.15 → 400 × 1.15 = ₹460 ✅
- 15% decrease → × 85/100 = × 0.85 → 400 × 0.85 = ₹340 ✅
WHY yeh kaam karta hai? Original (100%) + badhotri (15%) = 115%, yaani nayi value original ka 115% hai. Kami mein 100% − 15% = 85% bachta hai. Dono tareekon ka jawab hamesha same aata hai, bas multiplier wala ek hi step mein ho jaata hai.
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🔐 Deep Concept: Same ₹2, Alag Percentage!
Samosa ₹10 se ₹12 hua: increase = 2/10 × 100 = 20%.
Ab socho, agle mahine samosa wapas ₹12 se ₹10 ho gaya. Kya yeh 20% decrease hai?
Decrease = 2, par ab original ₹12 hai! To % decrease = 2/12 × 100 = 200/12 = 16 2/3 % (lagbhag 16.67%).
| Badlaav | Change | Original (base) | Percentage |
|---|---|---|---|
| ₹10 → ₹12 | ₹2 | ₹10 | 20% increase |
| ₹12 → ₹10 | ₹2 | ₹12 | 16 2/3 % decrease |
WHY alag? Change dono baar ₹2 hai, par jis number se divide karte hain (base) badal gaya. Bade base pe wahi ₹2 chhota hissa lagta hai.
Ek aur gehri baat: Increase 100% se zyada ho sakta hai (₹10 → ₹25 = 150% increase, Post 6 yaad karo). Par marks, keemat, logon ki ginti jaisi cheezon mein decrease 100% se zyada nahi ho sakta, kyunki 100% decrease matlab value 0 ho gayi, isse neeche ye ja hi nahi sakti.
Golden rule: Har baar poochho, “Shuruaat kahan se hui?” Wahi base hai, wahi neeche aayega.
sirf charumam.com readers ke liye 🔐
✏️ Solved Examples
Example 1 (Easy): Pichhle saal Class 8 mein 40 bachche the. Is saal 46 hain. Kitne percent badhe?
Original = 40, New = 46 → New bada hai, to increase.
Increase = 46 − 40 = 6
% Increase = 6/40 × 100 = 600/40 = 15%
WHY sahi hai? Check: 40 ka 15% = 0.15 × 40 = 6, aur 40 + 6 = 46 ✅. Humne original (40) se divide kiya, kyunki badhotri pichhle saal ki ginti se shuru hui.
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Example 2 (Medium): Aapke papa ka ₹240 wala mobile recharge plan 12.5% mehnga ho gaya. Ab plan kitne ka hai?
Tareeka 1: 12.5% = 1/8 (Post 5 wali yaad). 240 ka 1/8 = 240 ÷ 8 = ₹30. Nayi keemat = 240 + 30 = ₹270.
Tareeka 2 (multiplier): 100% + 12.5% = 112.5% → × 1.125 → 240 × 1.125 = ₹270.
WHY sahi hai? Dono tareekon se ₹270 aaya. Ulta check: 30/240 × 100 = 12.5% ✅. “Mehnga” shabd batata hai ki jodna hai, ghatana nahi.
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Example 3 (NCERT style): Ek kasbe ki aabaadi 2020 mein 25,000 thi aur 2024 mein 28,000 ho gayi. Usi kasbe mein ped 1,250 se ghatkar 1,000 reh gaye. (i) Aabaadi kitne percent badhi? (ii) Ped kitne percent ghate?
(i) Increase = 28,000 − 25,000 = 3,000. % Increase = 3,000/25,000 × 100 = 3/25 × 100 = 12%.
(ii) Decrease = 1,250 − 1,000 = 250. % Decrease = 250/1,250 × 100 = 1/5 × 100 = 20%.
WHY sahi hai? Check: 25,000 ka 12% = 3,000 ✅, aur 1,250 ka 20% = 250 ✅. Dono baar original (2020 wali ginti) se hi divide kiya. Aabaadi badhi par ped ghate: soch ke dekho, yeh kasbe ke liye achhi khabar hai ya chinta ki baat? 🌳
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Ab Kabir aur Zoya dono expert: Badlaav ko hamesha original se naapo! 🎉
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🏠 Real Life Mein Percentage Increase aur Decrease
- 🛍️ Sale: “Sab kuch 20% off!” yaani keemat 20% ghati. ₹500 ki T-shirt → 500 × 0.80 = ₹400.
- 🏏 Cricket: Pichhle match mein team ke 150 runs, is match mein 180. Increase = 30/150 × 100 = 20%.
- 📱 Mobile data: Roz 2 GB use karte the, ab 3 GB. Increase = 1/2 × 100 = 50%. Itna zyada? Thoda screen time pe dhyaan dein! 😄
- 🌾 Kheti: Pichhle saal ek khet mein 40 quintal gehun, is saal 46 quintal. Increase = 6/40 × 100 = 15%.
- ⚡ Bijli ka bill: Garmi mein 300 unit, sardi mein 240 unit. Decrease = 60/300 × 100 = 20%.
Har jagah ek hi formula: (Change ÷ Original) × 100.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Kya karein | Kyun |
|---|---|---|
| “Kitne percent badha / ghata?” (dono values di hain) | ✅ (Change ÷ Original) × 100 | Badlaav ko shuruaati value se naapna hai |
| “15% badha, nayi value?” (original aur % diya hai) | ✅ Original ka 15% nikaalo aur jodo, ya × 1.15 | Badhotri original ke 15% jitni hai |
| Sirf “kitne rupaye / kitne log badhe” poocha ho | ❌ Percentage nahi, seedha New − Original | Sawaal ginti maang raha hai, dar nahi |
| New value se divide karna | ❌ Kabhi nahi (jab tak sawaal khud na kahe) | Base hamesha original hota hai |
— 📌 charumam.com
❌→✅ Worked Mistake
Sawaal: Ek pen ki keemat ₹50 se ghatkar ₹40 ho gayi. Kitne percent kam hui?
❌ Galat: “Decrease = 50 − 40 = 10. % Decrease = 10/40 × 100 = 25%.”
Galti kya hai? Bachche ne new value (40) se divide kar diya. Par keemat ₹50 se ghatni shuru hui thi, to base ₹50 hai.
✅ Sahi:
- Decrease = 50 − 40 = ₹10
- % Decrease = 10/50 × 100 = 20%
Check karne ka tareeka: ₹50 ka 20% = ₹10, aur 50 − 10 = ₹40 ✅. Agar 25% sahi hota, to 50 ka 25% = 12.50 ghatkar ₹37.50 aata, ₹40 nahi. ❌
Yaad rakho: Jawab nikaalne ke baad hamesha ulta check karo: original ka utna % jodo/ghatao, new value aani chahiye.
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📝 10 MCQs
Q1. Percentage increase nikaalte waqt change ko kisse divide karte hain?
Solution dekho
Sahi jawab: (b)
- (a) galat: badlaav new value se shuru nahi hua, isliye woh base nahi hai.
- (b) sahi: badlaav original se shuru hua, isliye (Change ÷ Original) × 100.
- (c) galat: change ÷ change = 1 hamesha, isse kuch pata nahi chalta.
- (d) galat: 100 se guna karte hain, divide nahi; aur divide original se hota hai.
Q2. Ek game ki keemat ₹80 se ₹100 ho gayi. Kitne percent badhi?
Solution dekho
Sahi jawab: (b)
- (a) galat: 20 ko new value 100 se divide kar diya (20/100). Base galat.
- (b) sahi: Increase = 20. 20/80 × 100 = 25%. Check: 80 ka 25% = 20, 80 + 20 = 100 ✅
- (c) galat: 80 to original keemat hai, percent nahi.
- (d) galat: 100/80 × 100 = 125% batata hai ki nayi keemat original ka 125% hai. Increase to 125% − 100% = 25% hi hai.
Q3. Ek class mein 60 bachche the, ab 45 reh gaye. Kitne percent ghate?
Solution dekho
Sahi jawab: (b)
- (a) galat: 15 to bachchon ki ginti mein kami hai, percent nahi.
- (b) sahi: Decrease = 60 − 45 = 15. 15/60 × 100 = 1/4 × 100 = 25%.
- (c) galat: 15/45 × 100 = 33 1/3 %, yaani new value (45) se divide kar diya.
- (d) galat: 45/60 = 75% batata hai ki kitne bache, kitne ghate nahi.
Q4. ₹500 ki ghadi ki keemat 20% badh gayi. Nayi keemat kya hai?
Solution dekho
Sahi jawab: (c)
- (a) galat: 20% ki jagah ₹20 jod diye.
- (b) galat: yeh 20% kam hone pe aata, par keemat badhi hai.
- (c) sahi: 500 ka 20% = 100. 500 + 100 = ₹600. (Ya 500 × 1.2 = 600.)
- (d) galat: ₹100 sirf badhotri hai, nayi keemat nahi.
Q5. Ek school library mein 1,200 kitaabein thi. Purani hone ki wajah se 15% hata di gayi. Ab kitni bachi?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 1,200 ka 15% = 180. 1,200 − 180 = 1,020. (Ya 1,200 × 0.85 = 1,020.)
- (b) galat: 180 jod diye, jabki kitaabein hatayi gayi thi.
- (c) galat: 15% ki jagah sirf 15 kitaabein ghata di.
- (d) galat: 180 to hatayi gayi kitaabein hain, bachi hui nahi.
Q6. Kisi value ko 8% badhane ke liye use kis number se guna karein?
Solution dekho
Sahi jawab: (c)
- (a) galat: × 0.08 se sirf badhotri (8%) milti hai, nayi value nahi.
- (b) galat: 0.92 = 92%, yeh 8% ghataane ka multiplier hai.
- (c) sahi: 100% + 8% = 108% = 108/100 = 1.08.
- (d) galat: 1.8 = 180%, yaani 80% increase.
Q7. Kisi value ko 0.75 se guna karna matlab:
Solution dekho
Sahi jawab: (b)
- (a) galat: 75% increase ka multiplier 1.75 hota.
- (b) sahi: 0.75 = 75%. Nayi value original ka 75% hai, yaani 100% − 75% = 25% ghati.
- (c) galat: 75% decrease mein sirf 25% bachta, multiplier 0.25 hota.
- (d) galat: increase ka multiplier 1 se bada hota hai, 0.75 to 1 se chhota hai.
Q8. Pen ₹15 se ₹18 ka hua. Notebook ₹40 se ₹46 ki hui. Kiski keemat zyada percent badhi?
Solution dekho
Sahi jawab: (a)
- (a) sahi: Pen: 3/15 × 100 = 20%. Notebook: 6/40 × 100 = 15%. 20% > 15%.
- (b) galat: rupayon ki badhotri compare ki, original keemat ko ignore kiya.
- (c) galat: 20% aur 15% barabar nahi.
- (d) galat: notebook 15% hi badhi, par pen ki 20% badhotri usse zyada hai.
Q9. Kisi cheez ki keemat 100% ghat jaaye, to nayi keemat kya hogi?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 100% ghatna = poori keemat ghat gayi. Multiplier = 100% − 100% = 0.
- (b) galat: aadhi keemat 50% decrease pe hoti.
- (c) galat: double 100% increase pe hota.
- (d) galat: utni hi tab rehti jab 0% badlaav ho.
Q10. Ek batsman ne pichhle season 400 runs banaye. Is season usne 30% zyada runs banaye. Is season ke runs?
Solution dekho
Sahi jawab: (d)
- (a) galat: 30% ki jagah sirf 30 runs jod diye.
- (b) galat: 120 sirf badhotri hai, kul runs nahi.
- (c) galat: yeh 30% kam hone pe aata (400 − 120).
- (d) sahi: 400 ka 30% = 120. 400 + 120 = 520. (Ya 400 × 1.3 = 520.)
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❓ FAQs (Bachchon Ke Asli Sawaal)
1. Original se hi divide kyun? New se karein to kya hoga?
Percentage hamesha “kisi cheez ka” hota hai. “Keemat 20% badhi” ka matlab hai pehle wali keemat ka 20% badhi. Agar new se divide karoge to aap ek alag sawaal ka jawab de rahe ho (“badhotri nayi keemat ka kitna hissa hai?”), jo poocha hi nahi gaya. Worked Mistake mein dekha: base badalte hi 20% ka 25% ho gaya!
2. Kya increase 100% se zyada ho sakta hai? Aur decrease?
Increase ho sakta hai: ₹10 ka samosa ₹30 ka ho jaaye to increase = 20/10 × 100 = 200%. Par keemat, ginti, marks jaisi cheezein 0 se neeche nahi jaa saktin. 100% decrease matlab value 0 ho gayi, isliye inmein decrease 100% se zyada nahi hota.
3. ₹2 ka badlaav kabhi bada, kabhi chhota kaise?
Kyunki percentage original ke hisaab se naapta hai. ₹10 ki cheez pe ₹2 = 20%, par ₹200 ki cheez pe ₹2 = sirf 1%. Jaise ek chhote bachche ke liye 2 kg wazan badhna bahut hai, par ek bade aadmi ke liye kam. Base jitna bada, utna hi chhota percentage.
4. Agar 10% badhaayein aur phir 10% ghataayein, to kya wapas wahi number aayega?
Nahi! ₹100 pe 10% badha → ₹110. Ab 10% ghata, par ab base ₹110 hai: 110 ka 10% = 11, to 110 − 11 = ₹99. Dusri baar ka base badal gaya, isliye jawab ₹100 nahi aaya. Aise “ek ke baad ek” percentages ki aur mazedaar baatein hum Post 13 (Tricky Percentages) mein karenge.
5. Multiplier (× 1.15, × 0.85) kyun seekhein, jab do step wala tareeka bhi kaam karta hai?
Dono sahi hain. Multiplier ek hi step mein jawab de deta hai aur calculator pe bahut tez hai. Saath hi yeh soch saaf karta hai: “15% badha” = “nayi value original ki 115% hai”. Aage Growth aur Compounding (Post 11) mein yahi multiplier bahut kaam aayega.
6. Kaise pata karein ki sawaal increase ka hai ya decrease ka?
Do tareeke: (1) Values dekho: new > original to increase, new < original to decrease. (2) Shabd dekho: “badha, mehnga, zyada, upar gaya” = increase; “ghata, sasta, kam, off, discount” = decrease. Jawab likhte waqt “badha” ya “ghata” zaroor likho.
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🏋️ Practice Zone (12 Sawaal)
Q1. Easy Ek value 50 se 60 ho gayi. Kitne percent badhi?
Solution dekho
Increase = 60 − 50 = 10. % Increase = 10/50 × 100 = 20%.
Check: 50 ka 20% = 10, 50 + 10 = 60 ✅
Q2. Easy Ek value 80 se 60 ho gayi. Kitne percent ghati?
Solution dekho
Decrease = 80 − 60 = 20. % Decrease = 20/80 × 100 = 1/4 × 100 = 25%.
Check: 80 ka 25% = 20, 80 − 20 = 60 ✅
Q3. Easy 300 ko 10% badhao.
Solution dekho
300 ka 10% = 30 (Post 4 wali trick: 10% = 10 se divide). 300 + 30 = 330.
Q4. Easy ₹200 ki kitaab pe 5% chhoot mili. Kitne ki padi?
Solution dekho
200 ka 5% = 10 (10% = 20, uska aadha = 10). 200 − 10 = ₹190.
Q5. Medium Ek colony ki aabaadi 2,400 se badhkar 2,760 ho gayi. Kitne percent badhi?
Solution dekho
Increase = 2,760 − 2,400 = 360. % Increase = 360/2,400 × 100 = 36,000/2,400 = 15%.
Check: 2,400 ka 15% = 360 ✅
Q6. Medium Bus ka kiraya ₹45 se ₹54 ho gaya. Kitne percent badha?
Solution dekho
Increase = 54 − 45 = 9. % Increase = 9/45 × 100 = 1/5 × 100 = 20%.
Q7. Medium ₹18,000 ka TV sale mein 12% sasta mila. Kitne ka mila?
Solution dekho
18,000 ka 12% = 18,000 × 12/100 = 180 × 12 = 2,160. Nayi keemat = 18,000 − 2,160 = ₹15,840.
Multiplier se: 18,000 × 0.88 = 15,840 ✅
Q8. Medium Ek paudhe ki lambai ek mahine mein 36 cm se 45 cm ho gayi. Kitne percent badhi?
Solution dekho
Increase = 45 − 36 = 9 cm. % Increase = 9/36 × 100 = 1/4 × 100 = 25%.
Dhyaan do: 9/45 × 100 = 20% galat hoga, kyunki base 36 cm (shuruaati lambai) hai.
Q9. NCERT style Petrol ka daam ₹96 prati litre se ₹102 prati litre ho gaya. Kitne percent badha?
Solution dekho
Increase = 102 − 96 = ₹6. % Increase = 6/96 × 100 = 1/16 × 100 = 100/16 = 6.25%.
Check: 96 ka 6.25% = 96 × 6.25/100 = 6 ✅
Q10. NCERT style Ek school mein 1,250 students the. Agle saal admission 8% badh gaye. Ab kitne students hain?
Solution dekho
1,250 ka 8% = 1,250 × 8/100 = 100. Ab students = 1,250 + 100 = 1,350.
Multiplier se: 1,250 × 1.08 = 1,350 ✅
Q11. NCERT style Ek shehar mein ek saal mein “kharab hawa” (poor air quality) wale din 120 the. Ped lagaane ki muhim ke baad agle saal yeh 90 reh gaye. Kitne percent kami aayi?
Solution dekho
Decrease = 120 − 90 = 30. % Decrease = 30/120 × 100 = 1/4 × 100 = 25%.
Yahan decrease achhi khabar hai! 🌳
Q12. NCERT style Chawal ₹48 prati kg tha. Daam 25% badh gaya. (i) Naya daam kya hai? (ii) Ab 5 kg chawal kitne ka aayega?
Solution dekho
(i) 48 ka 25% = 48 ÷ 4 = 12. Naya daam = 48 + 12 = ₹60 prati kg. (Ya 48 × 1.25 = 60.)
(ii) 5 kg = 5 × 60 = ₹300.
Answer Key — charumam.com exclusive
🧠 HOTS (Sochne Wale Sawaal)
Q1. Ek school bag ki keemat 20% badhne ke baad ₹360 ho gayi. Meena kehti hai, “Purani keemat = 360 − 360 ka 20% = 360 − 72 = ₹288.” Kya Meena sahi hai? Sahi purani keemat kya thi?
Solution dekho
Meena galat hai. 20% purani keemat pe badha tha, nayi (₹360) pe nahi.
Purani keemat = 100% maano. Badhne ke baad = 120% = ₹360. To 1% = 360 ÷ 120 = 3, aur 100% = ₹300.
Check: 300 ka 20% = 60, 300 + 60 = 360 ✅. Meena ka ₹288 check karo: 288 ka 20% = 57.60, 288 + 57.60 = 345.60, ₹360 nahi. ❌
Q2. Raju ki lambai ek saal mein 150 cm se 165 cm hui. Sonu ki lambai 120 cm se 135 cm hui. Dono 15 cm badhe. Kya dono ki badhotri “barabar” kahi jaayegi?
Solution dekho
cm mein barabar (15 cm), par percentage mein nahi:
Raju: 15/150 × 100 = 10%. Sonu: 15/120 × 100 = 12.5%.
WHY: Sonu ki shuruaati lambai kam thi, isliye wahi 15 cm uske liye bada hissa hai. “Kitne cm” poocha ho to barabar, “kitni tezi se / kitne percent” poocha ho to Sonu aage.
Q3. Samosa ₹10 se ₹12 hua (20% increase). Phir ₹12 se wapas ₹10 hua. Aryan kehta hai, “Yeh bhi 20% decrease hai.” Kya woh sahi hai?
Solution dekho
Nahi. Doosri baar original ₹12 hai. Decrease = 2, % Decrease = 2/12 × 100 = 50/3 = 16 2/3 %.
WHY: Change same (₹2) hai, par base badal gaya (10 se 12). Bade base pe wahi ₹2 chhota percentage banta hai.
Q4. Ek number ko 20% ghataane pe 64 milta hai. Woh number kya hai?
Solution dekho
Number = 100% maano. 20% ghataane ke baad 80% bacha = 64.
1% = 64 ÷ 80 = 0.8, to 100% = 80.
Check: 80 ka 20% = 16, 80 − 16 = 64 ✅. (Dhyaan do: 64 + 64 ka 20% = 76.8 galat hota, kyunki 20% 64 ka nahi, original number ka tha.)
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🏆 Olympiad Corner
Q1. Ek dukaan ne January mein 240 pen beche. February mein January se 25% zyada beche. March mein February se 30 pen kam beche. January ke muqable March mein bikri kitne percent badhi?
Solution dekho
February = 240 ka 125% = 240 × 1.25 = 300. March = 300 − 30 = 270.
January se March: Increase = 270 − 240 = 30. % Increase = 30/240 × 100 = 12.5%.
WHY: Sawaal “January ke muqable” poochh raha hai, isliye base January (240) hai, February nahi.
Q2. Ek class mein 25 ladke aur 20 ladkiyan hain. 5 nayi ladkiyan admission leti hain. (i) Ladkiyon ki sankhya kitne percent badhi? (ii) Poori class kitne percent badhi?
Solution dekho
(i) Ladkiyan: 5/20 × 100 = 25%.
(ii) Class pehle 45 thi, ab 50. Increase = 5/45 × 100 = 100/9 = 11 1/9 % (lagbhag 11.11%).
WHY alag? Badhotri dono mein 5 hai, par base alag hai: ladkiyon ka 20, class ka 45.
Q3. Ek cheez ki keemat ₹100 se 30% badhkar ₹130 ho gayi. Ab keemat ko kitne percent ghataayein ki wapas ₹100 ho jaaye?
Solution dekho
Ab original ₹130 hai aur ₹30 ghataane hain.
% Decrease = 30/130 × 100 = 300/13 = 23 1/13 % (lagbhag 23.08%).
Check: 130 × (300/13)/100 = 30, aur 130 − 30 = 100 ✅. Jawab 30% nahi, kyunki base ab ₹130 hai.
Q4. Ek tanki mein 800 litre paani tha. 35% paani use ho gaya. Phir usmein shuruaati paani (800 litre) ke 20% jitna paani daala gaya. Ab tanki mein kitna paani hai, aur shuruaat ke muqable kitne percent kam hai?
Solution dekho
Use hua = 800 ka 35% = 280. Bacha = 800 − 280 = 520.
Daala = 800 ka 20% = 160. Ab = 520 + 160 = 680 litre.
Decrease = 800 − 680 = 120. % Decrease = 120/800 × 100 = 15%.
Check: 35% gaya, 20% aaya, dono 800 ke hi: 35% − 20% = 15% ✅ (yahan dono percent ek hi base ke hain, isliye seedha ghata sakte hain).
sirf charumam.com readers ke liye 🔐
💗 CharuMam Motivation
Agar aap roz 20 minute padhte ho aur use 25 minute kar do, to sirf 5 minute ka farak hai, par yeh 25% increase hai! Chhoti si badhotri bhi percentage mein badi hoti hai, jab shuruaat chhoti ho.
Isliye chhoti shuruaat se mat ghabraao. Aaj thoda, kal thoda zyada. Har din poore focus se padho, mehnat mein kami mat aane do, aur sabr rakho, kyunki badhotri dheere-dheere dikhti hai. Aur haan, kisi din marks ghat jaayein, to yaad rakho: decrease bhi sirf ek number hai, agla increase aapke haath mein hai! 🌟
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🟢 Master Recap
- Pehle dekho: new > original to increase, new < original to decrease.
- Change = badi value − chhoti value.
- % Change = (Change ÷ Original) × 100. Base hamesha original, kabhi new nahi.
- Samosa ₹10 → ₹12 = 20% badha, chips ₹20 → ₹23 = 15% badha. Samosa zyada tezi se mehnga hua.
- % diya ho to nayi value: original ka p% nikaalo, increase mein jodo, decrease mein ghatao.
- Multiplier: p% increase → × (100 + p)/100, p% decrease → × (100 − p)/100. Jaise 15% badha → × 1.15, 15% ghata → × 0.85.
- Same change, alag base → alag percentage (₹10 → ₹12 = 20%, par ₹12 → ₹10 = 16 2/3 %).
- Hamesha ulta check karo: original ka utna % jodo/ghatao, new value aani chahiye.
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👉 Aage Kya?
Ab aap kisi bhi cheez ka percentage increase aur decrease nikaal sakte ho. Ab socho, dukaandaar ₹80 mein cheez khareed ke ₹100 mein bechta hai, to usne kitne percent kamaaya? Yahi “original pe percentage” wali soch agle post mein Profit aur Loss mein kaam aayegi! 🚀
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬